GK Chesterton once said that mathematicians and chess players go mad, whereas poets do not—or rarely do so, anyway. He was wrong about that; actually, poetry is related to mathematics—it is about rhythm, and rhythm is number. So poets probably go mad as often as mathematicians; perhaps someone could compile the statistics…Really, Chesterton was caught in the art versus science dialectic, with his contention—his retreat—for his God, the being God, found in “sane” art versus “mad” science. As so often with Chesterton, he was being perverse to get attention; everyone knows that both poets and mathematicians are mad more often than not.
Why do mathematicians go mad, though? Well, mathematicians go mad in a particular way; they usually become paranoid and withdrawn—often they claim that people are engaged in a plot against them and want to poison their food. Men to have exhibited this behaviour include: Cantor, Gödel, Brouwer, Nash, and Bobby Fischer—obviously, not every mathematician goes this way; just more than average, and particularly the very talented ones. So mathematicians suffer from a particular madness—mistrust.
Of course, they mistrust because they are right to mistrust. Mathematics is about consistency—as with logic—and human beings are not very consistent, to say the least. A less charitable way to say that humans are inconsistent is to say that we are disloyal—we tend to betray. Mathematicians are better able than most to infer what humans really intend; if you pay attention to what people do, not what they say, then their true character will be revealed—and even the way they construct their sentences, since language has a logic to it, will reveal what they really want or are about.
What humans are really about—even the most apparently upstanding and respectable—often turns out to deeply disturb. Indeed, humans are often engaged in “games” that might be obscure even to their conscious mind but are not obscure to mathematicians. Nash, of course, developed Game Theory; and this has many uses, yet is most notable for its use as a tool to determine optimal behaviour and also predict behaviour—to address the underlying “game” behind human interactions or interactions between states, or between any “actor”. To see so deeply and clearly, as it turns out, can be an experience that disturbs, since you will see quite how malicious and deceptive humans are.
Accordingly, mathematicians struggle to trust anyone; they struggle for consistency in their work—and also certainty; and humans offer neither. Hence Gödel, if someone wanted to see him whom did not want to see, did not not make an excuse; rather, he made an appointment to see that person at a specific time and place—then he avoided that place and time. He said it was the only way to be sure he would not accidentally meet that person elsewhere—consistent and certain.
Martin Luther said that God must exist because there must be at least one being man can trust—not a real argument for God, but a definite summary as to the human condition. If you want something you can trust get a dog—or God, the two being related. So mathematicians might overstate the case as regards how much you can trust a person when they sink into paranoia—on the other hand, they probably see more acutely than most quite how untrustworthy humans are. Notably, there are no great female mathematicians; and this is because women are not consistent enough to be mathematicians—hence most religions mistrust women more than men, though men are bad enough; the Moslem law states two women are worth a man’s testimony in court. Mathematics itself is mysticism; it was required to enter the old Academy and in ancient Greek it etymologically relates to “the mantis”—the rishi, or “seer”, in Hindooism. The mystic, as with the mathematician and the poet, often isolates himself to work—he isolates himself from the lies and betrayal; he is the outsider.